Trying to bend my mind to Julia's way

@LStoleriu wrote:

Hi everyone,

I’m a C&Maple physicist trying to learn the “true” Julia way of solving problems.
As a small project I’m trying to solve a nonlinear equation doing something like that:

using NLsolve

Nsteps = 101

Hk = 1.0
FieldMax = 3.0 * Hk
FieldMin = -FieldMax
H = FieldMax

theta_H = 45.0 * π / 180.0
theta_0 = 15.0 * π / 180.0

function f!(F, x)
    F[1] = Hk * cos(x[1]) * sin(x[1]) + H * sin(x[1] - theta_H)
end

function j!(J, x)
    J[1, 1] = Hk * (cos(x[1])^2 - sin(x[1])^2) + H * cos(x[1] - theta_H)
end

theta = nlsolve(f!, j!, [ 0.5 ])
println(theta.zero)
println(converged(theta))

This works great, but now I’d like to solve the same equation for Nsteps different values of H and store the results in an array called M.
I was able to do that using a C-like approach, by continuing the program like that:

M = zeros(Nsteps)
H_range = collect(range(FieldMax, length=Nsteps, stop=FieldMin))

function SWsolve(H_range, M)
    i = 0
    for H_loco in H_range
        global H = H_loco
        theta = nlsolve(f!, j!, [ 0.5 ])
        i = i+1
        M[i] = cos(theta_H - theta.zero[1])
    end
end

SWsolve(H_range, M)
hyst = plot(H_range, M)
display(hyst)

I tried a lot to simplify this using Julia-like constructions but I failed (for example, I tried to remove the for loop from the SWsolve() function while using the dot(".") operator to pass the H_range elements) but I failed.

Can you suggest a more efficient way of doing this?

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